Tough question - it all depends how you want to ride. I ride a hartail and full suspension bike and like both and do both on the same trails but generally, if the downhills are steeper, gnarly, more technical, I want my fully. And although I'm riding a fully, I have friends doing the some trails and downhills on rigid singlespeeds.
The general difference between HT and fully is that with a HT your legs and arms become the bike's suspension. You can tire out quicker and you can't usually ride as fast because you need to be up out of the saddle using your legs when if riding a fully, you can still sit and pedal. HT's are lighter and generally better hill climbers but the new shocks allow for lockout or "propedal" cycling which aids in climbing.
Anyway, if considering a fully, try to keep the design simple, fewer pivot points. Consider mechanical not hydraulic disc brakes or better yet V-brakes because they are easier to use and maintain.
Hopefully you know of a bike shop and/or mechanic you can trust to ask questions.
A good fully to consider, not alot of money, but easily upgraded is Specialized FSR. Stay with the basic model** and skip the hydraulic disc brakes. The components and wheels can later be upgraded. Price is around $1650 - 2000.
**basic model has mechanical disc brakes.